Another relation among the neutrino mass-squared differences?

Abstract

Determining absolute neutrino masses remains a central challenge in particle physics. Relations among the neutrino mass-squared differences could facilitate this determination and shed additional light on the underlying mass-generation mechanism. Inspired by recent global fits of neutrino oscillation parameters, we propose a simple algebraic relation between $\Delta m^2_{21}$ and $\Delta m^2_{31}$. It provides a framework to analytically manipulate these parameters and admits specific physical interpretations. In particular, the results may point toward a vanishing $\nu_1$ mass.